A MATHEMATICAL MODEL FOR AN ASSOCIATIVE MEMORY

A mathematical model for an associative memory is proposed that uses associative addressing and distributed storage. Associative addressing is accomplished by mapping from a space with relatively few dimensions (input variables) to the vertices of a binary-valued hypercube embedded in a much higher dimensional space. The dimension of the image space is chosen to be sufficiently grent that a hyperplane can be passed through the origin such that the relative distances to the image points are the relative functional values that are to be stored. The distributed memory is achieved in the n-tuple representation of the hyperplane, since each element will in general be used in calculating the distance to many points (images), and hence in storing many functional values. A technique formulated for solving the large linear systems that arise in such a problem and a proof of the convergence of such a procedure are included. Unfortunately, the basic form of an associative memory imposes the restriction that only a single linear expression be available at any one time, and that further its relation to other expressions not be known. This generally imposes a iurther restriction that the linear expressions be randomly drawn from the linear system and returned. Typically these systems have many more variables than equations. Several examples of the behavior of the associative memory as simulated on a CDC 1604 computer and of the convergence properties of the algorithm proposed here to solve the associated linear systems are considered. (auth